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Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group

Author

Listed:
  • Aleksejus Mihalkovich

    (Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
    These authors contributed equally to this work.)

  • Matas Levinskas

    (Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
    These authors contributed equally to this work.)

  • Eligijus Sakalauskas

    (Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
    These authors contributed equally to this work.)

Abstract

In this paper, we present a counter mode of a Shannon block cipher based on the matrix power function. We make use of the matrix power function to define a single round symmetric cipher. Continuing our previous research, we implement a non-commuting group the order of which is a power of two in order to define a CTR mode in its most classic interpretation. We explore the security of the newly defined scheme, first, by showing that our block cipher is perfectly secure and does not leak any information about the initial plaintext based on the ciphertext. Then, we define a sequence of security games that show how the CTR mode of our cipher can resist all passive attacks.

Suggested Citation

  • Aleksejus Mihalkovich & Matas Levinskas & Eligijus Sakalauskas, 2022. "Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3363-:d:916454
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    References listed on IDEAS

    as
    1. Lina Dindiene & Aleksejus Mihalkovich & Kestutis Luksys & Eligijus Sakalauskas, 2022. "Matrix Power Function Based Block Cipher Operating in CBC Mode," Mathematics, MDPI, vol. 10(12), pages 1-24, June.
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